Abstract

We consider discrete time versions of two classical problems in the optimal control of admission to a queueing system:(i) optimal routing of arrivals to two parallel queues and (ii) optimal acceptance/rejection of arrivals to a single queue. We extend the formulation of these problems to permit a k step delay in the observation of the queue lengths by the controller. For geometric inter-arrival times and geometric service times the problems are formulated as Controlled Markov Chains with expected total discounted cost as the minimization objective.
For problem (i) we show that when k = 1, the optimal policy is to allocate an arrival to the queue with the smaller expected queue length (JSEQ: Join the Shortest Expected Queue) For $k\geq2$, however, JSEQ is not optimal.
For problem (ii) we show that when k = 1, the optimal policy is a threshold policy. There are, however, two thresholds $m_0\geq$$m_l>0$, such that $m_0$ is used when the previous action was to reject, and $m_1$ is used when the previous action was to accept.

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Conference Paper

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